一类新型Szasz-Kantorovich-Bezier算子在Orlicz空间内的逼近  

On approximation of a new type of Szasz-Kantorovich-Bezier operator in Orlicz spaces

作　　者：孙芳美 吴嘎日迪[1] Sun Fangmei Wu Garidi(College of Mathematics Science, Inner Mongolia Normal University, Huhhot 010022, China)

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022

出　　处：《纯粹数学与应用数学》2017年第2期168-176,共9页Pure and Applied Mathematics

基　　金：国家自然科学基金(11161033);内蒙古自治区研究生科研创新资助项目(S20161013501)

摘　　要：研究了一类新型Szasz-Kantorovich-Bezier算子在Orlicz空间内的逼近问题.在连续函数空间和L_p空间内研究算子逼近方法的基础上,利用函数逼近论中的常用方法和技巧以及K泛函、Ditzian-Totik模、Holder不等式、Cauchy不等式、凸函数的Jensen不等式等工具得到了该算子在Orlicz空间内的逼近正定理、逆定理和等价定理.由于Orlicz空间包含连续函数空间和L_p空间,其拓扑结构也比L_p空间复杂得多,所以本文的结果具有一定的拓展意义.In this paper we investigate the approximation problem of a new type of Szasz-Kantorovich-Bezier operator in Orlicz spaces based on the methods of studying the operator approximation in continuous function space and Lp space, and used common measures and techniques in function approximation theory. K-functional modulus of Ditzian-Totik, Holder inequality, Cauchy inequality, the convex property of N-function,Jensen inequality are used as tools to obtain direct throrem ,converse throrem and equivalence theorem in orlicz spaces Because the Orlicz space includes continuous function space and Lp space, and its topological structure is more complicated than Lp space, the results of this paper have certain expansion significance.

关 键 词：新型Szasz—Kantorovich—Bezier算子 ORLICZ空间 正定理 逆定理 等价定理 

分 类 号：O174.41[理学—数学]